SeCaV: A Sequent Calculus Verifier in Isabelle/HOL

Asta Halkjær From
(Technical University of Denmark)
Frederik Krogsdal Jacobsen
(Technical University of Denmark)
Jørgen Villadsen
(Technical University of Denmark)

We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof checker for our SeCaV derivations. The interactive features of Isabelle/HOL make our system transparent. For instance, the user can simply click on a side condition to see its exact definition. Our formalized soundness and completeness proofs pertain exactly to the calculus as exposed to the user and not just to some model of our tool. Users can also write their derivations in the SeCaV Unshortener, which provides a lighter syntax, and expand them for later verification. We have used both tools in our teaching.

In Mauricio Ayala-Rincon and Eduardo Bonelli: Proceedings 16th Logical and Semantic Frameworks with Applications (LSFA 2021), Buenos Aires, Argentina (Online), 23rd - 24th July, 2021, Electronic Proceedings in Theoretical Computer Science 357, pp. 38–55.
Published: 8th April 2022.

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